The non-linear post-Friedmann framework and Einstein’s signature in large-scale structure

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Non-linear structure formation at scales much smaller than the Hubble horizon is traditionally studied with Newtonian methods, for instance N-body simulations, while early Universe and horizon scales perturbations are investigated with relativistic perturbation theory. In view of new large scale galaxy surveys that will provide data with an unprecedented accuracy, it is timely to bridge the gap between these different approaches, going beyond the Newtonian approximation and unifying the study of the very large scales and the non-linear scales in a single theoretical framework.
In this talk I will describe the post-Friedmann framework, a sort of post-Minkowskian (weak field) approach to cosmology, such that at leading order in a 1/c expansion Newtonian cosmology is recovered as a consistent approximate solution of Einstein equations, on top of a Friedmannian background. In this framework, linear and non-linear relativistic contributions appear at next order. Resumming variables and linearising the equations one recovers first-order relativistic perturbation theory, i.e. the framework is valid on horizon scales and beyond.
I will illustrate the first practical application, i.e. the extraction of the frame-dragging gravitomagnetic potential from N-body simulations, and its power spectrum. Similarly, the difference between the two scalar potential, known as “slip” in cosmology, can also in principle be computed, sourced at leading order by purely Newtonian non-linear terms. I will also present relativistic non-Gaussian corrections to the initial conditions in Newtonian simulations that arise at second order in perturbation theory.